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Journal of Lightwave Technology

Study of the complex atomic susceptibility of erbium-doped fiber amplifiers

E. Desurvire

Published Jan 1, 1990• 138 citations
Publisher

Abstract

A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.>

DOI
10.1109/50.59191

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A basic understanding of the susceptibility of fiber amplifiers (SOFA) is required to undertake device optimization, e.g., for uses in optical communications systems. In recent work Desurvire1 has developed a semiclassical treatment of the SOFA for erbium-doped fiber amplifiers (EDFAs) taking account of the Stark splitting of the energy levels in the Er-doped glass. That work, which utilized the standard Kramers-Kronig relationships, was applicable to the unsaturated regime of operation. In this contribution, generalized Kramers-Kronig relations2 are utilized to obtain analytical expressions for the SOFA valid even in the saturation regime. It is then shown how, given experimentally measurable absorption cross-sections, the SOFA may be calculated in any operating conditions. In this way gain and refractive-index changes occurring in EDFAs may be deduced, again having universal validity.

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Comments on “Study of the Complex Atomic Susceptibility of Erbium-Doped Fiber Amplifiers”

Jean-Fran�ois Bisson, Dmitrii Kouznetsov

This comment aims to report and correct a mistake in the paper by Desurvire (J. Lightw. Technol., vol. 8, no. 10, pp. 1517-1527, Oct. 1990) with regard to the expression of the complex susceptibility of quasi-three-level laser systems. The derived susceptibility formula contradicts the assumption of thermal equilibrium between sublevels within each manifold and leads to the wrong conclusion that the real and imaginary parts of the susceptibility of saturated materials do not verify the Kramers-Kronig relations (KKR). The corrected formula for the susceptibility is hereby proposed. The poles of the susceptibility obtained with the new formula are all located in the upper half plane of the complex plane, in accordance with the principle of causality. Hence, the KKR should be valid in the saturated regime.

Journal of Lightwave Technology•Jan 1, 2008•1 citation

Signal-induced refractive index changes in erbium-doped fiber amplifiers

M. Janos, S.C. Guy

This paper reports the measurement and analysis of signal power-induced changes in the refractive index spectrum of an aluminosilicate erbium-doped fiber amplifier (EDFA). For a constant 980 nm pump power of 11 mW, a 1553 nm signal power of 4.6 mW caused a peak-to-trough change in refractive index of (3.8/spl plusmn/0.4)/spl times/10/sup -8/ across the EDFA gain spectrum. A Kramers-Kronig transform of the signal-induced change in absorption coefficient agreed well with the measured change in refractive index. This result conflicts with the behavior of the system predicted by a homogeneously broadened two-level model and suggests limitations in the representation of the Er/sup 3+/:glass system by a discrete set of homogeneously broadened transitions.

Journal of Lightwave Technology•Apr 1, 1998•25 citations
A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.>
A basic understanding of the susceptibility of fiber amplifiers (SOFA) is required to undertake device optimization, e.g., for uses in optical communications systems. In recent work Desurvire1 has developed a semiclassical treatment of the SOFA for erbium-doped fiber amplifiers (EDFAs) taking account of the Stark splitting of the energy levels in the Er-doped glass. That work, which utilized the standard Kramers-Kronig relationships, was applicable to the unsaturated regime of operation. In this contribution, generalized Kramers-Kronig relations2 are utilized to obtain analytical expressions for the SOFA valid even in the saturation regime. It is then shown how, given experimentally measurable absorption cross-sections, the SOFA may be calculated in any operating conditions. In this way gain and refractive-index changes occurring in EDFAs may be deduced, again having universal validity.
A detailed model for the complex susceptibility behavior of erbium-doped amplifiers, which applies in the saturation regime of operation, is presented. The model takes into account the effective individual laser transitions between the upper and lower manifolds. The model is based on a curve fitting algorithm that fits the emission and absorption cross section with Voigt lineshapes, which correspond to the effects of both homogeneous and inhomogeneous line broadenings. Experimental measurements show that the model accurately predicts the susceptibility in the saturation regime. The sensitivity of the model susceptibility predictions to the Stark-split energy level data is shown to be minor, as long as the number of transition wavelengths used is high. Results show the full spectral behavior of the complex susceptibility of an integrated optical erbium-doped amplifier in the saturation regime and show that signal-induced changes in refractive index of up to around 1.6/spl times/10/sup -6/ can be obtained with a few milliwatts of signal change by driving the amplifier into saturation.
This comment aims to report and correct a mistake in the paper by Desurvire (J. Lightw. Technol., vol. 8, no. 10, pp. 1517-1527, Oct. 1990) with regard to the expression of the complex susceptibility of quasi-three-level laser systems. The derived susceptibility formula contradicts the assumption of thermal equilibrium between sublevels within each manifold and leads to the wrong conclusion that the real and imaginary parts of the susceptibility of saturated materials do not verify the Kramers-Kronig relations (KKR). The corrected formula for the susceptibility is hereby proposed. The poles of the susceptibility obtained with the new formula are all located in the upper half plane of the complex plane, in accordance with the principle of causality. Hence, the KKR should be valid in the saturated regime.
This paper reports the measurement and analysis of signal power-induced changes in the refractive index spectrum of an aluminosilicate erbium-doped fiber amplifier (EDFA). For a constant 980 nm pump power of 11 mW, a 1553 nm signal power of 4.6 mW caused a peak-to-trough change in refractive index of (3.8/spl plusmn/0.4)/spl times/10/sup -8/ across the EDFA gain spectrum. A Kramers-Kronig transform of the signal-induced change in absorption coefficient agreed well with the measured change in refractive index. This result conflicts with the behavior of the system predicted by a homogeneously broadened two-level model and suggests limitations in the representation of the Er/sup 3+/:glass system by a discrete set of homogeneously broadened transitions.